>That's four samples out of an infinite domain. To fully verify the function f via science you technically need infinite test cases to verify the fact. Usually you can never achieve this in reality so science usually takes what you call a "sample" and you say that if the sample is true very likely the hypothesis is true. The only assumption science makes is that probability theory applies to events in reality.

Usually equating null-hypothesis significance testing with the scientific method is a sign of cargo cult.